In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties...In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties. In this paper, we extend these results to general linear methods and to more generalproblem class Kστ. The concepts of (k, p, q)-secondary stability and (k, p. q)-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraicstability conditions while retaining the virtues of a nonlinear test problem.展开更多
The exponentially expanded space grid was incorporated into the network approach to overcome the problem of low simulation efficiency during the simulations of electrochemical problems with stiff kinetics or wide disp...The exponentially expanded space grid was incorporated into the network approach to overcome the problem of low simulation efficiency during the simulations of electrochemical problems with stiff kinetics or wide dispersion of diffusion coefficients, resulting in an effective electrochemical simulation method: exponentially expanded grid network approach (EEGNA). The stability and accuracy of the EEGNA for the simulation of various electrode processes coupled with different types of homogeneous reactions were investigated.展开更多
文摘In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties. In this paper, we extend these results to general linear methods and to more generalproblem class Kστ. The concepts of (k, p, q)-secondary stability and (k, p. q)-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraicstability conditions while retaining the virtues of a nonlinear test problem.
文摘The exponentially expanded space grid was incorporated into the network approach to overcome the problem of low simulation efficiency during the simulations of electrochemical problems with stiff kinetics or wide dispersion of diffusion coefficients, resulting in an effective electrochemical simulation method: exponentially expanded grid network approach (EEGNA). The stability and accuracy of the EEGNA for the simulation of various electrode processes coupled with different types of homogeneous reactions were investigated.
